本論文研究目標致力於探討Lorenz方程式變數和參數的物理意義。於1963年，美國學者Lorenz以自然對流的數學模型為基礎，推導簡化而得著名的Lorenz方程式，以其混沌現象而為人所知，混沌現象表示系統有不規則的週期運動，以及對初始條件有高敏感性。過去文獻探討Lorenz方程式大多侷限於其穩定性分析，或者是混沌現象的動態分析，卻鮮少有文獻深究此方程式對應於自然對流模型的物理意義。
首先，本論文將由自然對流模型之原始偏微分方程式推導到Lorenz之常微分方程式，包括其假設、推導過程，以及模擬驗證，在瞭解Lorenz方程式之後，為了找出Lorenz方程式與原始偏微分方程式之間參數與變數的關聯性。本論文接著利用同樣的推導過程，逐步分別忽略自然對流的黏度、浮力或是熱擴散效應，以獲得變形的常微分方程式，再透過分析這三組新方程式來推論變數與上述的物理意義之間的關係。最後藉著非線性被動理論(passivity theory)以及已知的物理定義，以定義Lorenz方程式變數的物理意義。
本論文提出假說，論述Lorenz方程式的三個常微分方程式變數之物理意義，分別代表自然對流系統的動能、熱位能，與總能，並利用各種數學分析或者是科學理論闡明之。未來可藉由實驗更進一步驗證，並預期將此分析方法應用於其他已知的混沌系統。

New physical insight into the variables and parameters of nonlinear Lorenz equations are discussed in this work. In 1963, the equations are derived from the model of natural convection by Lorenz and are noted for chaotic motion. The chaos means system has an irregular motion, and is sensitive to initial conditions. The Lorenz equations have been studied in many papers, which are focus on the stability and the chaotic dynamics. However, the physical implication comparing the Lorenz equations with natural convection attracts little attention in past literatures.
Therefore, first step is to derive the Lorenz equations which are ordinary differential equations from the original partial differential equations of natural convection, including assumptions, the derivation, and the simulation results. Then, derive the Lorenz equations again with different forced conditions, which are viscosity, buoyancy, and diffusion. With respect to the simulations of the modified Lorenz equations, observe the relation between the variables and the forced conditions. At last, due to the nonlinear passivity theory and known physical implication, propose the physical insight into the variables and parameters of the Lorenz equations.
The study propose that the variables of Lorenz equations, x, y, z, are kinetic energy, thermodynamic potential energy, and total energy respectively. Use kinds of method or theory to prove it. Moreover, it’s better to verify the insight by experiment in the future. Expect that the analysis method applies to the known chaotic systems.

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